A way to improve our ability to detect static magnetic fields is to use double quantum magnetometery (DQ) which works by first preparing an equal superposition of the \(m_{s}=|+1\rangle \)  and \(|m_{s}=-1\rangle \)  states (for example, \(|+_{DQ}\rangle =(1/\sqrt{2})(|+1\rangle +|-1\rangle )\) ), which is then exposed to a magnetic field during the free precession interval followed by the final population being mapped to the \(|m_{s}=0\rangle \)  state. Use of DQ magnetometery allows for several advantages. In the previously used single quantum (SQ) basis, nonmagnetic noise sources such as temperature fluctuations, electric-field noise, and inhomogeneous strain may also contribute to spin dephasing. However, values of \(T_{2,ens}^{*}\)  in the DQ basis are insensitive to these common-mode noise sources. Furthermore, the phase accumulation doubles for DQ magnetometry since \(\Delta m_{s}=+2\)  although the dephasing time also doubles resulting in \(T_{2,DQ}^{*}\approx T_{2,SQ}^{*}/2\)  (for our simulations, we have used \(T^{*}_{2,DQ}=1.3\mu s\) ). However, for isotopically purified, low nitrogen diamond, \(T_{2,DQ}^{*}\)  can actually exceed the coherence time in the SQ basis [1]}, thereby allowing us to benefit from the doubled phase factor and increased coherence time. This is demonstrated in Fig.REF , where we can see a much higher level of confidence is achieved as compared to Fig. REF .
